Relating large $U_{e3}$ to the ratio of neutrino mass-squared differences

TL;DR

This paper explores how the sizable $U_{e3}$ neutrino mixing element can be linked to the ratio of neutrino mass-squared differences, proposing models with texture zeros and zero neutrino mass to explain this relationship.

Contribution

It introduces a novel connection between $U_{e3}$ and neutrino mass-squared differences, and constructs explicit flavor symmetry models embodying this link.

Findings

$U_{e3}$ correlates with the ratio of solar and atmospheric mass-squared differences.

Models with texture zeros and zero neutrino mass can realize this relation.

Explicit flavor symmetry models predicting these features are developed.

Abstract

The non-zero and sizable value of $U_{e3}$ puts pressure on flavor symmetry models which predict an initially vanishing value. Hence, the tradition of relating fermion mixing matrix elements with fermion mass ratios might need to be resurrected. We note that the recently observed non-vanishing value of $U_{e3}$ can be related numerically to the ratio of solar and atmospheric mass-squared differences. The most straightforward realization of this can be achieved with a combination of texture zeros and a vanishing neutrino mass. We analyze the implications of some of these possibilities and construct explicit flavor symmetry models that predict these features.